Rigidity Results for the p-Laplacian Poisson Problem with Robin Boundary Conditions

Abstract

AbstractLet $$\Omega \subset \mathbb {R}^n$$ Ω ⊂ R n be an open, bounded and Lipschitz set. We consider the Poisson problem for the p-Laplace operator associated to $$\Omega $$ Ω with Robin boundary conditions. In this setting, we study the equality case in the Talenti-type comparison: we prove that the equality is achieved only if $$\Omega $$ Ω is a ball and both the solution u and the right-hand side f of the Poisson equation are radial and decreasing.